1. Percentiles and Box-and- Whisker Plots
Definitions
Percentiles and Box-and- Whisker Plots

2. Goals Today Interpret the meaning of percentile scores
Compute the median, quartiles, and five-number summary from raw data
Make a box-and-whisker plot
Interpret the results of a box-and-whisker plot
Describe how a box-and-whisker plot indicates spread of data about the median

3. Definitions
Pth Percentile - a value such that P% of the data fall at or below it and (100-P)% of the data fall at or above it.

4. Definitions
Pth Percentile - a value such that P% of the data fall at or below it and (100-P)% of the data fall at or above it.
Examples?

5. Definitions
Cards

6. Definitions Quartile - Percentiles that divide the data into fourths
First Quartile Q1 is the 25th percentile
First Quartile Q2 is the 50th percentile
First Quartile Q3 is the 75th percentile
Cards

7. Definitions Calculate Quartile Order the data from smallest to largest
Find the median. This is the second quartile
The First Quartile Q1 is then the median of the lower half of the data; that is, it is the median of the data falling below the Q2 position (and not including Q2)
The third quartile Q3 is the median of the upper half of the data; that is, it is the median of the data falling above the Q2 position (and not including Q2).
Cards

8. Definitions
Cards

9. Definitions Interquartile range, (IQR) - Q3 - Q1
Five- Number Summary -
Lowest Value Q1
Median Q3
Highest Value
Cards

10. Definitions
Box-and-Whisker Plot - A graphic sketch of the data using the five numbers
Cards

11. How to make a box-and-whisker plot
Definitions
How to make a box-and-whisker plot
Draw a vertical scale to include the lowest and highest data values
To the right of the scale, draw a box from Q1 to Q3
Include a solid line through the box at the median level
Draw vertical lines, called whiskers, from to the lowest value and from Q1 to the highest value Q3
Cards

13. Pg , 15
Pg , 2, 7

14. Definitions Population Mean = = Σx/N
Population Variance = = Σ(x )2 / N
Population Standard Deviation = = Σ(x )2 / N
Cards

15. “Quiz” Please calculate the x Median Mode Range S2 S n
For the Following set of data:
1, 1, 3, 3, 3, 4

16. Definitions
Coefficient of variation (CV) - The standard deviation as a percentage of the sample or population
For a Sample
CV = (s / x)*100%
For a Population
CV = ( / )* 100%
Cards

17. Definitions
Chebyshev’s Theorem - For any set of data and for any constant k greater than 1, the proportion of the data that must lie within k standard deviations on either side of the mean is at least:
1- 1/(k2)
Cards

18. Group Project Get into groups of around 5
Decide a piece of information you want to find
Something You can calculate
Mean
Median
Mode
Pick a method for collecting your sample
Sampling type
Time

19. Group Project (Requirements)
Organize your data for me to check (Google Sheets, excel)
Data points
What is your population?
What is your sample?
How did you sample?
Make a Frequency Distribution Table
You pick number of classes
Draw a histogram
Central Points: Mean, Median, Mode
Measurements of Variation: Range, Variance, Standard Deviation, Coefficient of Variation
Define your Chebychev intervals
75%
88.9%
93.8%
Create a Five-Number Summary (if possible)
Draw Box-and-Whisker Plot

20. Group Project Presentation
Communicate your topic
Explain topic
Display Graphs
Powerpoint
ELMO
Highlight key information
Draw conclusions from data
Infer something about your population